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My bare bookshelves are crying out for the addition of a new family member, more specifically a book:

  1. Discussing the classical Klein-Gordon field, spinor fields, gauge fields and all other matter fields in a generally co-variant fashion.

  2. Discussing of the Schrodinger (non-relativistic scalar) field.

  3. Detailing the application of fields to things like inflation, dark matter, condensed matter etc.

  4. Possessing nice, thorough derivations (like the single-particle, relativistic Lagrangians from the complex scalar field) and other such items of interest which show how single-particle mechanics follow from classical fields. Discussion of conformal symmetries, first class and second class constraints are also desired.

  5. With some discussion of field quantization.

I have possession of some papers covering these topics and some books (like Landau's Classical Theory of Fields), but they are outdated, restricted to EM fields and very often bypass all discussion of classical fields to quantize them right away. Since I asked for a generally co-variant approach, there should be extensive co-ordinate free representations.

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Note that saying that your question isn't opinion-based doesn't make it not opinion-based. (In fact, saying "please don't close this" or something to that effect correlates quite well with being close-worthy.) That being said, under the new (upcoming) book recommendation policy, it's possible this would be allowed, so let's see what others say. – David Z Oct 30 '13 at 19:46
Isn't the idea of applying non-quantum theories to things like inflation kind of defeating the point? – Danu Oct 30 '13 at 19:46
@DavidZ Fair enough. But I have placed very specific requirements for the book, so I really doubt there is much scope for open-ended discussion. – dj_mummy Oct 31 '13 at 4:00
@Danu Inflation fields are used, though I don't know anything about them. I edited my question. – dj_mummy Oct 31 '13 at 4:35
Have you had a look at 'Classical Theory of Gauge Fields' by Valery Rubako? – user32008 Oct 31 '13 at 18:40
up vote 2 down vote accepted

Some of the topics you mentioned seem to be discussed in this book:

Mark Burgess, Classical Covariant Fields, Cambridge University Press, 2005

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